Here is the full list of all 58 Day of the Tentacle Remastered achievements. It takes around 5-6 hours to unlock all of the achievements on Windows.
Get all other achievements in the game
Play the whole game without skipping a cutscene
Hoagie uses battery with Chron-o-John instead of plug
Try to alter the contract with Booboo-B-Gone
Try to sign the contract yourself with the quill pen
Talk to Washington, Jefferson, or Hancock while they're outside
Laverne tries the chattering teeth on her human during the human show
Sit through the end credits
Defeat Purple Tentacle yesterday
Cook the hamster in Maniac Mansion (Don't try this at home, kids!)
Reach yesterday without turning the stereo off
Power Laverne's Chron-o-John
Vacuum up a hamster
Get a tiny sweater
Win the human contest
Acquire a diamond
Get Fred to sign the contract
Wake up Dr. Fred
Ask the IRS agents if they're related
Return the stamp album to Weird Ed
Pick up 45 things that don't belong to you
Try to swap the textbook with the stamp album
Disqualify Harold
Try to wash the dirty car with the brush
Power Hoagie's Chron-o-John
Red makes a super battery with only a little help from Hoagie
Make vinegar
Laverne thinks about eating the cat
Deflate Oozo
Enter the human contest
Try to mix the red paint and the Booboo-B-Gone
Squirt five different people with disappearing ink
Try to mix the disappearing ink with Booboo-B-Gone
Ring the front desk bell 100 times
Try to microwave the hamster again after he's thawed out
Microwave the frozen hamster
Try to put something metal in the microwave
Make a skunk
Flush 50 objects through time
Get a job
Make it rain
Get all six novelty items
Open the safe
Try to mix the decaf and caffeinated coffees
Hoagie eats a Hoagie
Talk to Dead Cousin Ted with all three kids
Pick up 30 things that don't belong to you
Clothe Laverne in the costume
Change the flag
Try to flush the hamster
Climb through the chimney with all three kids
Destroy a cherry tree
Create a cherry tree
Pick up 15 things that don't belong to you
Play Maniac Mansion
Close a door
Turn off the television
Find Fred's basement workshop